Thune, the Republican Policy Committee chairman and fourth-ranking GOP Senator, revealed Tuesday that he would not seek his party’s presidential nomination, although he left the door open to reconsider. The ambitious South Dakotan is likely to focus instead on climbing higher on Capitol Hill and, in doing so, add to the Senate Republican Conference’s intraparty fight for leadership advancement.

According to sources, Thune could soon join the crowded race for GOP Whip, the No. 2 position in the party leadership. He also is giving strong consideration to running for Conference Chairman, the No. 3 slot. Given that other Senators have already announced their candidacies for those positions, Thune’s entrance might not be far behind.

Within hours of Kyl’s retirement announcement, Senate Republican Conference Chairman Lamar Alexander (Tenn.) and National Republican Senatorial Committee Chairman John Cornyn (Texas) launched their candidacies for Whip, which will open in January 2013.

Sen. Mike Johanns (Neb.) then revealed that he would run for Conference Chairman, and Conference Vice Chairman John Barrasso (Wyo.), the fifth-ranking Republican, confirmed that he was interested in moving up. Other Senators could be eyeing the leadership openings as well.

GOP Senators are attempting to downplay the competition for leadership roles so far in advance of the 113th Congress. Sources say the campaigns are likely to occur quietly, at least for the next year. But any action Thune takes to catch up to his quickly moving colleagues could temporarily restart the jockeying and even exacerbate it by leaving his No. 4 leadership position up for grabs.